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Friday, 1 November 2013

A Medieval and an Elizabethan Maths Book

Love it or loathe it maths is a useful skill. This week I
thought I’d seek out what the Cathedral library has in terms of historic maths
books and found two gems. The first treasure is Anianus’ Computus cum commento (Computus with commentary), a late fifteenth-century
arithmetic manual with instructions and demonstrative woodcuts. This short
guide was printed in Paris by Guy Marchant in 1497, and the Worcester Cathedral
library copy is the only one surviving in the UK.

Anianus, the author of the commentary, is a figure whom we
know little about, but some believe he was a French Benedictine monk. He wrote
his computus guide at the end of the fourteenth-century and numerous manuscript
copies survive. It was so popular in the century that followed that the
commentary was printed in Paris, Rouen, Lyon and Basel. The title page of Marchant’s
1497 edition opens with this splendid woodcut:

Photograph, Compotus cum commento. Reproduced by the permission of the Dean and Chapter of Worcester Cathedral (U.K.)

This is just one of six woodcuts which link books to
Marchant’s workshop. It depicts two shoe makers working and includes a central
shield containing two hands holding open a book. At the top you can see an
abbreviated form of his motto “Sola fides suficit” ,“faith alone suffices”.

Computus, for those wondering, was the major form of mathematical
learning in the middle Ages. Put simply, it is the mathematical working out of
the dates of Lent and Easter for any given year. In Western Christianity,
Easter is the first Sunday after the first full moon after the spring equinox.
Once this date has been calculated, the rest of the church’s moveable festivals
and celebrations can be worked out in relation to this date. Historians of
mathematics have stressed the overwhelming complexity of early computus
manuals. Anianus’ compoutus manual was likely popular because it followed a
much simpler format than others on the subject, such as those written by Bede
and Arnold of Villanova. The commentary is written in prose, and explains how
to use the hand as a mnemonic device on which to calculate. Here are some of
the woodcuts from Marchant’s edition showing how to use the left hand:

Photograph, Compotus cum commento. Reproduced by the permission of the Dean and Chapter of Worcester Cathedral (U.K.)

Fast forward around a hundred and fifty years and we find
the second of the Cathedral library’s interesting maths books: A geometrical treatise named pantometria.
This Elizabethan geometry book, written by Thomas Digges c. 1570 presents an
array of technologies and tools developed in the Elizabethan era for the study
of mathematics and topographical work. Pictured below is one such tool, called a Theodelitus, which is described
as a “circle divided into 360 grades”, the diameter of which was 2 feet,
meaning that the sizeable instrument had to be held down by some type of clamp.

Reproduced by the permission of the Dean and Chapter of Worcester Cathedral (U.K.)

The tool is thought to have been invented by Digges’ father,
Leonard. Leonard Digges’ died when his son was aged thirteen and left a
partially completed manuscript copy of Pantometria
to his son. Thomas Digges completed his father's work. As a child Thomas Digges
became a ward of the renowned Elizabethan astronomer and mathematician, John
Dee, who you can find out about by clicking here.

What’s most interesting about Pantometria is the consistent application of geometry to solving military problems and war-related scenarios. Though composed
centuries apart, Pantometria is reminiscent
of the military-style textbooks produced for young school children in Nazi
Germany, which superimpose basic maths problems with militaristic images. If you
look at the woodcut below you can see how one problem is put in the
context of an observer trying to estimate how far two rather threatening looking,
incoming ships are away.

Reproduced by the permission of the Dean and Chapter of Worcester Cathedral (U.K.)

The woodcuts on folio 30 and 32 take on an even more militaristic framework, as you can see two warring parties firing canons at one another.

Photograph reproduced by the permission of the Dean and Chapter of Worcester Cathedral (U.K.)

We might read this textbook, therefore, as more than simply
an instructive manual, it’s constant references to spying, even in the more
innocent peeping Tom scenario, conjures to mind the network of
spies at home and abroad employed by Queen Elizabeth I during her reign. Many
of the geometry problems, particularly in the first part of the book, are aimed
at either seeing things you are usually unable to see, or visually penetrating
fortified areas. There is even this excellent woodcut of a man using the
reflection of a pond to spy on his wife situated several stories above.

Photograph reproduced by the permission of the Dean and Chapter of Worcester Cathedral (U.K.)

More broadly, the consistent references to sea faring and
sea voyages mean the book is clearly a product of the age of exploration. This
maths book then, might also be a useful source for military historians or
Elizabethan enthusiasts as it clearly reflects national concerns in this period.